As investigated by [1]}, the Bi-Lipschitz constant plays a fundamental role in the practical invertibility and numerical stability of NFs.
To understand the learned transformation \(T\)  in terms of its Lipschitz continuity, we propose to study the Lipschitz surface of \(T\) .
Note that if \(T\)  is differentiable and \(L\) -Lipschitz, we can follow the derivation by [1]} (in equation (5) and (6) therein) to approximate
\(L &= \sup _{{x}\in \operatorname{supp}({\mathbf {x}})}\Vert J_T({x})\Vert _2 = \sup _{{x}\in \operatorname{supp}({\mathbf {x}})} \sup _{\Vert {v}\Vert _2=1}\Vert J_T({x}){v}\Vert _2 \\ &\approx \sup _{{x}\in \operatorname{supp}({\mathbf {x}})} \sup _{\Vert {v}\Vert _2=1} \frac{1}{\varepsilon } \Vert T({x}) - T({x}+ \varepsilon {v}) \Vert _2 \hspace{5.0pt},\) 
